Error propagation in hybrid manipulators is addressed here within a rigorous mathematical framework. Understanding how errors propagate in serial manipulators and cascades of platform manipulators is important for developing better designs. In this paper we show that errors propagate by convolution on the Euclidean motion group, SE (3). When local errors are small, they can be described well as distributions on the Lie algebra se(3). We show how the concept of a highly concentrated Gaussian distribution on SE(3) is equivalent to one on se(3). Numerical examples illustrate that convolution and covariance propagation provide the same answers for small errors

A quantity of importance in coherent optical communications is the probability density of a filtered signal in the presence of phase noise (PN). The Fokker-Planck(FP) approach has been recognized as a rigorous way to describe these statistical properties. However, computational difficulties in solving these FP equation shave prevented their widespread application. In this paper, we present a new and simple computational solution method based on techniques from noncommutative harmonic analysis on motion groups. This proposed method can easily solve all the PN FP equations with any kind of intermediate frequency filter. We also present a new derivation of PN FP equations from the viewpoint of stochastic processes.

Error propagation on the Euclidean motion group arises in a number of areas such as errors that accumulate from the base to the distal end of manipulators. We address error propagation in rigid-body poses in a coordinate-free way, and explain how this differs from other approaches proposed in the literature. In this paper, we show that errors propagate by convolution on the Euclidean motion group, SE(3). When local errors are small, they can be described well as distributions on the Lie algebra se(3). We show how the concept of a highly concentrated Gaussian distribution on SE(3) is equivalent to one on se(3). We also develop closure relations for these distributions under convolution on SE(3). Numerical examples illustrate how convolution is a valuable tool for computing the propagation of both small and large errors

Hyper-redundant manipulators have a large number of redundant degrees of freedom. They have been recognized as a means to improve manipulator performance in complex and unstructured environments. However, the high degree of redundancy also causes difficulty in the calculation of workspaces and inverse kinematics. This paper develops a diffusion-based algorithm for workspace generation of hyper-redundant manipulators. This algorithm makes the workspace generation problem as simple as solving a diffusion equation which has an explicit solution. This diffusion equation is a partial differential equation defined on the motion group SE(N), and describes the evolution of the workspace density function, depending on manipulator length and kinematic properties. This paper also solves the inverse kinematics problem in an elegant way by dividing the manipulator into virtual segments and cascading the corresponding workspace densities generated by the diffusion equation.

Motivated by a physical phenomenon, the diffusion process, this paper develops a diffusion-based algorithm for workspace generation of highly articulated manipulators. This algorithm makes the workspace generation problem as simple as solving a diffusion-type equation which has an explicit solution. This equation is a partial differential equation defined on the motion group and describes the evolution of the workspace density function depending on the manipulator length and kinematic properties. Numerical simulations using this algorithm are also presented.

Presents an artificial potential field method for path planning of non-spherical single-body robots. The model simulates steady-state heat transfer with variable thermal conductivity. The optimal path problem is then the same as a heat flow with minimal thermal resistance. The novelty of this technique is that the thermal resistance in the configuration space for all different orientations of the robot can be superimposed. This reduces a search on R/sup n//spl times/SO(n) to one on R/sup n/ followed by a search on SO(n). Examples are presented to demonstrate the approach.